Question

find the measures of $angle e$, $angle g$, and $angle h$ if $mangle f = 65^{circ}$. use the keypad to enter your answers in the boxes. the measure of $angle e$ is degrees. the measure of $angle g$ is degrees. the measure of $angle h$ is degrees.

Explanation:

Step1: Assume angles relationship

Since no other information about the angles' relationship is given, if we assume that $\angle E,\angle F,\angle G,\angle H$ are angles around a point, the sum of angles around a point is $360^{\circ}$. If we assume $\angle E,\angle F,\angle G,\angle H$ are in a quadrilateral, the sum of interior - angles of a quadrilateral is $360^{\circ}$. But without more context, if we assume $\angle E$ and $\angle F$ are vertical angles (if the figure allows such an assumption), vertical angles are equal.
$m\angle E=m\angle F = 65^{\circ}$

Step2: Assume supplementary angles

If $\angle F$ and $\angle G$ are supplementary (adjacent and form a straight - line), then $m\angle G=180^{\circ}-m\angle F$.
$m\angle G = 180 - 65=115^{\circ}$

Step3: Assume another supplementary relationship

If $\angle G$ and $\angle H$ are supplementary (assuming a linear - pair relationship), then $m\angle H=180^{\circ}-m\angle G$.
$m\angle H=180 - 115 = 65^{\circ}$

Answer:

The measure of $\angle E$ is $65$ degrees.
The measure of $\angle G$ is $115$ degrees.
The measure of $\angle H$ is $65$ degrees.